Small Angle Scattering and the Cybotactic Theory, as Applied to Single-Component Glasses
Adrian C. Wright*

The random network and cybotactic theories of the structure of single-component glasses, such as SiO2 and GeO2, differ in respect of the frequency of occurrence, and the size, of
crystalline-like (cybotactic) groupings within their vitreous network, and hence of the expected form of the spatial fluctuations in their average number density,
ρ°. The early crystallite
models used by Bienenstock & Bagley [J. Appl. Phys. 37 (1966), 4840.] to calculate the expected form of the small angle scattering for a vitreous silica structure formed from discrete
crystallites are extended to include the cybotactic theory, with its much smaller difference in number density between the cybotactic groupings and the surrounding matrix, and it is
demonstrated that small-angle scattering data cannot exclude the presence of cybotactic groupings.

The RMS fluctuation in average number density, <Δρ2>½, in vitreous SiO2 and GeO2, calculated from the zero-Q limit of the static structure factor, S(Q), is compared to that predicted by
the above theories. Assuming a purely random network, exhibiting density fluctuations with a Gaussian distribution, it is shown that the probability of finding regions (cybotactic groupings)
with the density of the crystalline phase formed upon devitrification is much higher for vitreous SiO2 than for vitreous GeO2, but in both cases is higher than would be expected for such a
random network. Hence it is concluded that the networks of single-component glasses, such as vitreous SiO2 and GeO2, do indeed include cybotactic groupings, corresponding to this crystalline phase.